Which one of the following metal complexes is most stable?

🧠 More Chelate Rings = More Stable

The chelate effect: complexes with chelating (multidentate) ligands are more stable than those with monodentate ligands of similar donor type. Each chelate ring adds extra entropy stability.

Order of $\mathrm{NH_3}$ replacement by ethylenediamine (en):

$[\mathrm{Co(NH_3)_6}] < [\mathrm{Co(en)(NH_3)_4}] < [\mathrm{Co(en)_2(NH_3)_2}] < [\mathrm{Co(en)_3}].$

(0 rings $\to$ 1 ring $\to$ 2 rings $\to$ 3 rings.)

The most stable is $[\mathrm{Co(en)_3}]\mathrm{Cl_2}$ — three 5-membered chelate rings.

🗺️ Why Chelation Wins (the Entropy Story)

Replacing 2 $\mathrm{NH_3}$ by 1 en doesn't change the enthalpy much (Co–N bonds either way), but it increases the number of free particles in solution: 1 en displaces 2 $\mathrm{NH_3}$, so $\Delta n > 0 \Rightarrow \Delta S > 0$. Positive entropy → more negative $\Delta G$ → bigger formation constant.

⚡ The Ring-Counting Shortcut

When all four options have the same donor type (here, all-nitrogen), pick the option with the most chelate rings. Don't bother computing log K values — ring count alone settles the ranking 95% of the time.

⚠️ Bigger Ring ≠ More Stable

5-membered chelate rings are most stable. en gives 5-rings (M–N–C–C–N back to M). A 4-membered or 7-membered ring is less stable than 5. So "more rings" only beats "fewer rings" when ring sizes are comparable.

$\boxed{\text{Answer: (2) } [\mathrm{Co(en)_3}]\mathrm{Cl_2}}$